Project 2 - 2-Mode Networks - Airlines and Airports¶
Betsy Rosalen and Mikhail Groysman¶
Project Overview¶
- Identify a large 2-node network dataset—you can start with a dataset in a repository. Your data should meet the criteria that it consists of ties between and not within two (or more) distinct groups.
- Reduce the size of the network using a method such as the island method described in chapter 4 of social network analysis.
- What can you infer about each of the distinct groups?
Choosing the Data¶
We have decide to build on the flight data from OpenFlights.org that we used in our first project.
OpenFlights consists of the following datasets:
- Airports
- Airlines
- Routes
- Planes
- Schedules
We have choosen to use the Routes and Airports datasets to build our network. We will use Airline ID and Source Airport ID from the Routes dataset as our two nodes. Each route record will be an edge between the two ntypes of nodes and we will add weighting by the number of routes that each airine has leaving from each particular airport. We will get additional airport node attribute data from the Airports dataset.
Variables used from the Routes dataset:
- Airline ID - Unique OpenFlights identifier for airline (see Airline).
- Source airport ID - Unique OpenFlights identifier for source airport (see Airport)
Variables used from the Airports dataset:
- Name
- City
- Country
- IATA
- Latitude
- Longtitude
Data is saved as .DAT files. They are UTF-8 encoded.
Loading the Data¶
First import necessary packages for plotting graphs using NetworkX and Matplotlib and set up graph size parameters...
import networkx as nx
from networkx.algorithms import bipartite as bi
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import math
%matplotlib inline
Read in Routes data to a Pandas dataframe. We only need the Airline and Airport columns so we selected for just those two.
routes_raw = pd.read_csv("Project1_Data/routes.dat",
header=None, sep=",",
usecols=[0, 2],
names=['Airline', 'Airport'])
routes_raw=routes_raw.dropna()
routes_raw.head(15)
Add Weights to the Dataframe¶
We chose to count the number of routes for each eirline at each airport and use that as a weight for our airline to airport edges.
aa = routes_raw.copy()
aa['weight'] = aa.groupby('Airline')['Airport'].transform('count')
aa.head(10)
len(aa)
Get Additional Airport Data¶
airports_raw = pd.read_csv("Project1_Data/airports.dat",
header=None, sep=",",
usecols=[1, 2, 3, 4, 6, 7],
names=['Airport Name','City','Country','IATA', 'Latitude', 'Longitude'])
#airports_raw1=airports_raw[airports_raw.Country=='France']
airports_raw.head()
len(airports_raw)
aa_merged = airports_raw.copy()
aa_merged = pd.merge(aa,aa_merged,left_on='Airport',right_on='IATA',how='inner')
aa_merged.head()
airport_nodes = aa_merged[['Airport','Airport Name','City','Country','IATA','Latitude','Longitude']].drop_duplicates().sort_values(by='Airport')
Check for Airline Codes that Match Airport Codes¶
set(aa_merged['Airline']) & set(aa_merged['Airport'])
There are two three letter codes that are used for both airlines and airports, so we have to add differentiation to the names before adding these airport atributes to the graph or all our airlines will also get coded as airports... To keep things short and so we can still read out graph once it's plotted, we added just an L for airLines just to those two airline codes.
#aa_merged['Airline'] = 'L_' + aa_merged.Airline.map(str)
#aa_merged['Airport'] = 'P_' + aa_merged.Airport.map(str)
#airport_nodes['Airport'] = 'P_' + airport_nodes.Airport.map(str)
aa_merged['Airline'] = np.where(
aa_merged['Airline'].isin(['ABJ', 'IOS']),
'L_' + aa_merged.Airline.map(str),
aa_merged.Airline
)
set(aa_merged['Airline']) & set(aa_merged['Airport'])
aa_merged.head()
Create NetworkX Graph Object¶
First we will create a full bipartite network with both nodes.
B = nx.Graph()
B.add_nodes_from(aa_merged['Airline'], bipartite=0)
B.add_nodes_from(aa_merged['Airport'], bipartite=1)
B.add_weighted_edges_from([tuple(d) for d in aa_merged[['Airline','Airport','weight']].values])
nx.set_node_attributes(B, airport_nodes.set_index('Airport').to_dict('index'))
Let's double check if our attributes were saved in the graph data.
list(B.nodes(data=True))[:3]
list(B.nodes(data=True))[-2:]
B.get_edge_data('L_AER','P_KZN')
print(nx.info(B))
Set 'Top' and 'Bottom' Nodes¶
airline_nodes = {n for n, d in B.nodes(data=True) if d['bipartite']==0}
airport_nodes = set(B) - airline_nodes
Check if the Graph is Connected¶
nx.is_connected(B)
Check if the Graph is Bipartite¶
bi.is_bipartite(B)
Density¶
print(bi.density(B, airline_nodes))
print(bi.density(B, airport_nodes))
Use Island Method on the Bipartite Graph¶
The functions below will use the edge weights to trim the graph into subgraphs at different minimum weight levels. Any node not connected by at least one ede with the minimum weight will be cut from the graph. We used the textbook functions as a starter, but had to revise them to get them to work...
'''
# textbook function doesn't work...
def trim_edges(g, weight=1):
g2=nx.Graph()
for f, to, edata in g.edges(data=True):
if edata['weight'] > weight:
g2.add_edge(f, to, edata)
return g2
'''
def trim_edges(g, weight=1):
g2=nx.Graph()
my_list=[]
my_list1=[]
for f, to, edata in g.edges(data=True):
if edata['weight'] > weight:
my_list.append(f)
my_list1.append(to)
g2.add_edge(f,to,attr_dict={weight:edata['weight']})
g2.add_nodes_from(my_list, bipartite=0)
g2.add_nodes_from(my_list1, bipartite=1)
return g2
def island_method(g, iterations=5, weight=1):
weights = [edata['weight'] for f, to, edata in g.edges(data=True)]
mn=int(min(weights)) if int(min(weights)) > weight else weight
mx=int(max(weights))
#compute the size of the step, so we get a reasonable step in iterations
step=int((mx-mn)/(iterations-1))
return [[threshold, trim_edges(g, threshold)] for threshold in range(mn,mx,step)]
Run island_method function using 4 iterations and a minimum weight 'water line' of 350...¶
islands = island_method(B, 4, 350)
print('min weight - ', '# of nodes - ', '# of island subgraphs')
for i in islands:
# print the threshold level, size of the graph, and number of connected components
print(i[0], ' - ', len(i[1]), ' - ', len(list(nx.connected_component_subgraphs(i[1]))))
islands[1][0] # the first index refers to the threshold
islands[1][1] # the second index refers to the graph object
Graph the Largest 'Island' Subgraph - minimum weight level 350¶
def set_colors(G):
colors = []
for node, data in G.nodes(data=True):
if data['bipartite'] == 1:
colors.append('olivedrab') # Airports in Green
else:
colors.append('cornflowerblue') # Airlines in Blue
return colors
G0=max(nx.connected_component_subgraphs(islands[0][1]), key=len)
plt.rcParams["figure.figsize"] = (15,15) # set plot size
colors = set_colors(G0) # set colors
#weights = [math.log(edata['attr_dict'][200]) for f, t, edata in G0.edges(data=True)] # set weights
nx.draw(G0, with_labels=True, node_color=colors, node_size=200,
font_size=10, font_weight='bold', edge_color="skyblue", alpha=0.5)
We can start to see already how many airports are connected by a much smaller number of airlines (as we would expect). We can also see how airlnes serve as boundary spanners between airports.Let's raise the water level though to see if we can gain more insight...
Graph the Second Largest 'Island' Subgraph - minimum weight level 1061¶
G1=islands[1][1]
plt.rcParams["figure.figsize"] = (15,15) # set plot size
colors = set_colors(G1) # set colors
nx.draw(G1, with_labels=True, node_color=colors, node_size=200,
font_size=10, font_weight='bold', edge_color="skyblue", alpha=0.5)
Major airlines are starting to be visible with the airports that they connect. Many cliques are startig to develop and airlines are starting to show as boundary spanners. A higher water level may make it easier to pick out individual airlines and airports.
Graph the Third Largest 'Island' Subgraph - minimum weight level 1772¶
G2=islands[2][1]
plt.rcParams["figure.figsize"] = (15,15) # set plot size
colors = set_colors(G2) # set colors
nx.draw(G2, with_labels=True, node_color=colors, node_size=200,
font_size=10, font_weight='bold', edge_color="skyblue", alpha=0.5)
Here we can really start to see the 4 most influential airlines in the network:
- FR - Air France
- UA - United Airlines
- DL - Delta Air Lines
- US - US Airways
- AA - American Airlines
If there are any others they are still hidden in the graph. Air France clearly stands out as a boundary spanner in this graph.
Graph the Fourth Largest 'Island' Subgraph - minimum weight level 2483¶
G3=islands[3][1]
plt.rcParams["figure.figsize"] = (8,8) # set plot size
colors = set_colors(G3) # set colors
nx.draw(G3, with_labels=True, node_color=colors, node_size=200,
font_size=10, font_weight='bold', edge_color="skyblue", alpha=0.5)
In this last graph we can see that FR, Air France, is the most influential airline in the network.
Airport Node Projected Graph¶
# compute an affiliation network of the Airports
airports = bi.weighted_projected_graph(B, airport_nodes)
# Find the largest connected subgraph in the network
#users_subgraph = nx.connected_component_subgraphs(users)[0] # textbook code doesn't work
airports_subgraph = max(nx.connected_component_subgraphs(airports), key=len) # alternate method
airports_subgraph.name = "Airports"
print(nx.info(airports_subgraph))
Run island_method function using 3 iterations and a minimum weight 'water line' of 25...¶
airport_islands = island_method(airports_subgraph, 3, 25)
print('min weight - ', '# of nodes - ', '# of island subgraphs')
for i in airport_islands:
# print the threshold level, size of the graph, and number of connected components
print(i[0], ' - ', len(i[1]), ' - ', len(list(nx.connected_component_subgraphs(i[1]))))
Graph the Largest Airport Node 'Island' Subgraph - minimum weight level 25¶
APG0=airport_islands[0][1]
# set plot size
plt.rcParams["figure.figsize"] = (15,15)
nx.draw(APG0, with_labels=True, node_color='olivedrab', node_size=200,
font_size=10, font_weight='bold', edge_color="olivedrab", alpha=0.5)
Graph the Second Largest Airport Node 'Island' Subgraph - minimum weight level 49¶
APG1=airport_islands[1][1]
# set plot size
plt.rcParams["figure.figsize"] = (6,6)
nx.draw(APG1, with_labels=True, node_color='olivedrab', node_size=200,
font_size=10, font_weight='bold', edge_color="olivedrab", alpha=0.5)
LHR or Heathrow Airport in London, England stands out as a boundary spanner in this graph.
Graph the Third Largest Airport Node 'Island' Subgraph - minimum weight level 73¶
APG2=max(nx.connected_component_subgraphs(airport_islands[2][1]), key=len)
# set plot size
plt.rcParams["figure.figsize"] = (2,2)
nx.draw(APG2, with_labels=True, node_color='olivedrab', node_size=200,
font_size=10, font_weight='bold', edge_color="olivedrab", alpha=0.5)
Frankfurt am Main Airport in Frankfurt, Germany and Charles de Gaulle Airport (Roissy Airport) in Paris, France are the two most influential airports in our network.
Airline Node Projected Graph¶
# compute an affiliation network of the Airlines
airlines = bi.weighted_projected_graph(B, airline_nodes)
# Find the largest connected subgraph in the network
#users_subgraph = nx.connected_component_subgraphs(users)[0] # textbook code doesn't work
airlines_subgraph = max(nx.connected_component_subgraphs(airlines), key=len) # alternate method
airlines_subgraph.name = "Airlines"
print(nx.info(airlines_subgraph))
Run island_method function using 3 iterations and a minimum weight 'water line' of 50...¶
airline_islands=island_method(airlines_subgraph, 3, 50)
print('min weight - ', '# of nodes - ', '# of island subgraphs')
for i in airline_islands:
# print the threshold level, size of the graph, and number of connected components
print(i[0], ' - ', len(i[1]), ' - ', len(list(nx.connected_component_subgraphs(i[1]))))
Graph the Largest Airline Node 'Island' Subgraph - minimum weight level 50¶
ALG0=max(nx.connected_component_subgraphs(airline_islands[0][1]), key=len)
# set plot size
plt.rcParams["figure.figsize"] = (15,15)
nx.draw(ALG0, with_labels=True, node_color='cornflowerblue', node_size=200,
font_size=10, font_weight='bold', edge_color="skyblue", alpha=0.5)
Graph the Second Largest Airline Node 'Island' Subgraph - minimum weight level 192¶
ALG1=max(nx.connected_component_subgraphs(airline_islands[1][1]), key=len)
# set plot size
plt.rcParams["figure.figsize"] = (6,6)
nx.draw(ALG1, with_labels=True, node_color='cornflowerblue', node_size=200,
font_size=10, font_weight='bold', edge_color="skyblue", alpha=0.5)
The seven most influential airlines in the network in alphabetical order are:
- AA - American Airlines
- AF - Air France
- AZ - Alitalia
- DL - Delta Air Lines
- KL - KLM Royal Dutch Airlines
- UA - United Airlines
- US - US Airways
Graph the Third Largest Airline Node 'Island' Subgraph - minimum weight level 334¶
ALG2=max(nx.connected_component_subgraphs(airline_islands[2][1]), key=len)
# set plot size
plt.rcParams["figure.figsize"] = (2,2)
nx.draw(ALG2, with_labels=True, node_color='cornflowerblue', node_size=200,
font_size=10, font_weight='bold', edge_color="skyblue", alpha=0.5)
The two most influential airlines in the network are clearly US and AA corresponding to US Airways and American Airlines respectively. Interestingly these do not correspond to the most influential airline in the bipartite network graph above, which was FR for Air France.